Borel Measures and Hausdorff Distance

Gerald Beer, Luzviminda Villar
1988 Transactions of the American Mathematical Society  
In this article we study the restriction of Borel measures defined on a metric space X to the nonempty closed subsets CL(X) of X, topologized by Hausdorff distance. We show that a <r-finite Radon measure is a Borel function on CL(X), and characterize those X for which each outer regular Radon measure on X is semicontinuous when restricted to CL(X). A number of density theorems for Radon measures are also presented.
doi:10.2307/2001197 fatcat:cqmh5n4ubngkpnh7lyb2nsu37m